A008799 Molien series for group [2,6]+ = 226.

1, 0, 2, 0, 3, 0, 5, 1, 7, 2, 9, 3, 12, 5, 15, 7, 18, 9, 22, 12, 26, 15, 30, 18, 35, 22, 40, 26, 45, 30, 51, 35, 57, 40, 63, 45, 70, 51, 77, 57, 84, 63, 92, 70, 100, 77, 108, 84, 117, 92, 126, 100, 135, 108, 145, 117, 155, 126, 165, 135, 176, 145, 187, 155, 198, 165, 210, 176, 222, 187

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1,-1,-1,1).

Formula

G.f.: (1+x^7)/((1-x^2)^2*(1-x^6)).

a(n) = floor((n^2+3*n+21+7*(n+1)*(-1)^n)/24). - Tani Akinari, Jul 25 2013

G.f.: (1 -x +x^2 -x^3 +x^4 -x^5 +x^6)/( (1+x+x^2)*(1-x+x^2)*(1+x)^2*(1-x)^3 ). - R. J. Mathar, Dec

18 2014

Maple

seq(coeff(series((1+x^7)/((1-x^2)^2*(1-x^6)), x, n+1), x, n), n = 0..80);

Mathematica

CoefficientList[Series[(1+x^7)/((1-x^2)^2*(1-x^6)), {x, 0, 80}], x] (* G. C. Greubel, Sep 12 2019 *)
LinearRecurrence[{1, 1, -1, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 5, 1, 7}, 80] (* Harvey P. Dale, Apr 16 2022 *)

Prog

(PARI) my(x='x+O('x^80)); Vec((1+x^7)/((1-x^2)^2*(1-x^6))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^7)/((1-x^2)^2*(1-x^6)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008799_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^7)/((1-x^2)^2*(1-x^6))).list()
A008799_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 5, 1, 7];; for n in [10..80] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-6]-a[n-7]-a[n-8]+a[n-9]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A227093 A266772 A262064 * A325346 A325836 A011013

Adjacent sequences: A008796 A008797 A008798 * A008800 A008801 A008802

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Definition clarified by N. J. A. Sloane, Feb 02 2018

More terms added by G. C. Greubel, Sep 12 2019

Status

approved